Christie's an assassin under Donovan's hire and in general likes toying with people. Lisa is really confusing, it's thought that she might be undercover as a scientist in DOATEC to spy on them but idk. Rig is Donovan's son and works undercover on the rig.
Christie & Rig are antagonists, Lisa is questionable.
In DOA1 when Raidou crippled Hayate and put him in a coma, Kasumi left the village to kill him in revenge for her brother (which she then did). This broke the 'shinobi code' of her village somehow and she's no longer allowed to return and her clan charged Ayane and Hayate with killing her.